Is there such a thing as a 50/50 chance?

[John Salerno]

Hi everyone. I have something of a vague question to ask, so I'll try to make it as coherent as possible. I assume that with a perfectly balanced coin, for example, there really is a 50/50 chance of getting either heads or tails each time.

 

But my question deals with situations that may have extenuating circumstances. For example, let's say you ask somebody a physics question. The possible outcomes are that they will either know the answer or not know the answer. So is it safe to say that there is a 50/50 chance that they will either know it or not know it?

 

What if we are told that the person in question is a physicist? It may be impossible to calculate precise odds, but is it correct to say that the possibility of giving a right or a wrong answer is no longer 50/50, even though only one of those two outcomes is possible? Or am I not making a proper distinction between something here?

 

Finally, is there a technical name for this kind of phenomenon?

 

Thanks!

[Mr Skeptic]

Just because there are two possibilities doesn't imply a 50-50 chance. This is only true if there are two equally likely possibilities.

 

As for coins, the are usually tested for fairness, although a few coins have had significantly different than 50-50 chance.

[John Salerno]

Just because there are two possibilities doesn't imply a 50-50 chance. This is only true if there are two equally likely possibilities.

 

Ah, that makes sense. So, generally speaking, it's wrong to say that the chances of someone getting a yes/no question right is 50/50?

[Mr Skeptic]

Ah, that makes sense. So, generally speaking, it's wrong to say that the chances of someone getting a yes/no question right is 50/50?

 

Generally for guessing a correct answer the probability of people getting it right is different than 50-50, depending on the question and the people. Often it is more than 50-50, but sometimes it is less. For example, "Does the earth orbit the sun?" They can guarantee getting a 50-50 chance of getting the correct answer by flipping a coin and saying yes for heads and no for tails.

[John Salerno]

Generally for guessing a correct answer the probability of people getting it right is different than 50-50, depending on the question and the people. Often it is more than 50-50, but sometimes it is less. For example, "Does the earth orbit the sun?" They can guarantee getting a 50-50 chance of getting the correct answer by flipping a coin and saying yes for heads and no for tails.

 

I see. Is there a name for this, where an either/or answer doesn't really give a 50/50 chance, or is it not as big of a deal as I seem to think it is?

[ajb]

I see. Is there a name for this, where an either/or answer doesn't really give a 50/50 chance, or is it not as big of a deal as I seem to think it is?

 

I am not aware of any special name here.

 

As Mr Skeptic has said, because some system has two outcomes does not mean that each outcome is necessarily of equal probability.

 

If we ask a question with a Yes/No answer (or similar) to someone and they truly guess, i.e. pick one at random then they stand a 50/50 chance of getting it right. The point here is that they have to guess.

[lemur]

More likely there is a name for the particular logical fallacy that causes people to think any yes/no question has 50/50 odds of being yes or no. There's a 50% chance I will discover the name for it at some point in the future, maybe:)

[Mr Skeptic]

I see. Is there a name for this, where an either/or answer doesn't really give a 50/50 chance, or is it not as big of a deal as I seem to think it is?

 

Well you could call it "bias" or "knowledge". It depends on the question and the person being asked. For example, "is 1+1=2?" vs "do peanuts kill more people than do terrorists?".

 

The person can always make his odds a 50% chance by flipping a coin. Let's say we're dealing with a prediction so that the outcome isn't known for certain but has a 80% likelihood of being true and 20% likelihood of being false. Then flipping the coin gives you 50%*80% + 50%*20% = 50%*100% = 50%. The same will hold no matter what the probabilities of "yes" or "no" being the correct answer. Your odds are only 50% if you guess with no knowledge, and will be lower than 50% if you have mistaken knowledge and more than 50% if you have accurate knowledge.

[John Salerno]

Ok, it makes a lot more sense to me now. My reason for asking was because I was trying to formulate an argument. It's religious in nature but I don't want to turn this thread into anything other than a discussion of statistics, but I'd like to give the statement and see if it can be said that the answer is 50/50:

 

"That a god exists or does not exist is either true or false. Therefore, there is a 50/50 chance of either answer being correct."

 

Now, given what was discussed about likelihood, how would we apply that in a case like this, where there is a definite answer, but we may never actually know the answer? Does the answer to this proposition amount to nothing more than a guess? Or can certain facts be counted as making one or the other option more likely?

 

Or is this just an age-old discussion that will never submit itself to this type of analysis?

[Mr Skeptic]

"Either I will roll a 6 the next time I roll the dice, or I will not. Therefore the probability that I roll a 6 is 50%."

 

How about that one? To take it a step further, what are the odds that you can correctly guess the outcome? Are your odds of correctly guessing 50%?

[John Salerno]

"Either I will roll a 6 the next time I roll the dice, or I will not. Therefore the probability that I roll a 6 is 50%."

 

How about that one? To take it a step further, what are the odds that you can correctly guess the outcome? Are your odds of correctly guessing 50%?

 

That's a great analogy. The next step of my argument was going to move to that point, i.e. which possible god are we referring to. But maybe you've shown me that it's not good to separate the two propositions.

[ajkoer]

Yes, Probit Analysis.

 

In essence, the probability of a Bernoulli outcome (like default) is impacted by one or more variables. Not surprisingly, big in the financial literature.

 

See also Reliability Theory, which deals with a variety of stress related failures and appropriate statistical probability density functions.

[DrRocket]

Hi everyone. I have something of a vague question to ask, so I'll try to make it as coherent as possible. I assume that with a perfectly balanced coin, for example, there really is a 50/50 chance of getting either heads or tails each time.

 

But my question deals with situations that may have extenuating circumstances. For example, let's say you ask somebody a physics question. The possible outcomes are that they will either know the answer or not know the answer. So is it safe to say that there is a 50/50 chance that they will either know it or not know it?

 

What if we are told that the person in question is a physicist? It may be impossible to calculate precise odds, but is it correct to say that the possibility of giving a right or a wrong answer is no longer 50/50, even though only one of those two outcomes is possible? Or am I not making a proper distinction between something here?

 

Finally, is there a technical name for this kind of phenomenon?

 

Thanks!

 

One fact that has not been made clear in this thread is that the mathematical theory of probability starts with probabilities being given -- starts with a probability space which includes events ( a sigma algebra of measurable sets) and probabilities (a probability measure).

 

The actual determination of probabilities is either based on empirical models, statistics, or an outright assumption. Probability theory has nothing to say about the matter.

 

Probabilities can be almost anything subject to only a few basic constraints: the probability that at least one of all possible events occurs must be one; the probability any event must be non-negative and no greater than 1; the probability that at least one of countably many disjoint events occurs is the sum of the individual probabilities. If there are finitely many primitive events, any assignment of non-negative numbers that sum to 1 defines a legitimate probability space -- only outside considerations can determine if it is a physically accurate model.